On the Output of Nonlinear Systems Excited by Discrete Prolate Spheroidal Sequences

The discrete prolate spheroidal sequences (DPSSs)- A set of optimally bandlimited sequences with unique properties- A re important to applications in both science and engineering. In this work, properties of nonlinear system response due to DPSS excitation are reported. In particular, the sequences are shown to be approximately orthogonal after passing through a nonlinear, multiple-input multiple-output dynamical system under quite general conditions. This work quantifies these conditions in terms of constraints upon the higher-order generalized transfer functions characterizing the Volterra expansion of a MIMO system, the Volterra order of the system, and the DPSS bandwidth parameter $W$ and time-bandwidth parameter NW. The approximate system output orthogonality allows multiple-input, multiple-output characterization of the linear narrowband response of a nonlinear system using simultaneous, DPSS excitation.